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Experimental Studies |
1 From the Department of Radiology, Beth Israel Deaconess Medical Center and Harvard Medical School, 330 Brookline Ave, Boston, MA 02215. Received June 21, 2002; revision requested August 21; final revision received January 13, 2003; accepted January 27. Address correspondence to R.G.S. (e-mail: rsheiman@bidmc.harvard.edu).
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODS RESULTS DISCUSSIONAPPENDIX REFERENCES |
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MATERIALS AND METHODS: Controlled extravasation of contrast material–enhanced blood (CEB) from 140 to 180 HU and at varying rates (0.3–1.0 mL/min) was performed during a 30-second period by using a microcatheter system placed within the descending colon of 14 swine. CEB was immediately followed by extravasation of unopacified blood at the same location and rate during serial helical CT imaging of the extravasation site. Region-of-interest analysis allowed quantification of the dilution of extravasated CEB as a function of time that was then modeled mathematically based on iodine mass and volume balances. Nonlinear least squares analysis was performed to optimize fitting of the model to experimental data, with a maximum regression value (R2) of 1.0 indicating a perfect fit. This model enabled the computer simulation of CT imaging of multiple combinations of bleeding rates and CEB attenuation to determine the sensitivity of helical CT for depicting active colonic bleeding.
RESULTS: Sixteen swine examinations yielded 16 CEB dilution curves. An excellent fit of the model to each dilution curve was achieved, as indicated by a mean R2 value of 0.8402. Swine examinations alone showed that targeted CT could depict CEB as low as 111 HU extravasating at a rate of 0.3 mL/min. Simulations that were based on helical CT images with 5-mm collimation reconstructed every 3 mm and that used the model indicated bleeding rates below 0.4 mL/min are detectable, provided peak aortic enhancement reaches 100 HU.
CONCLUSION: Conservatively, helical CT has the potential to depict active colonic hemorrhage at rates of 0.5 mL/min or less.
© RSNA, 2003
Index terms: Animals • Colon, CT, 75.12115 • Computed tomography (CT), experimental studies • Hemorrhage, CT
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODS RESULTS DISCUSSIONAPPENDIX REFERENCES |
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Because of the inherent ability of CT to depict slight differences in attenuation, it theoretically should be an extremely sensitive noninvasive modality for depicting active lower GI tract bleeding. The application of CT for this purpose however, poses multiple logistical problems. For example, the minimum extent of enhancement of extravasated blood for detection and the time window for examination must be determined, because extravasated contrast material–enhanced blood (CEB) will be followed and diluted by unenhanced blood and hyperactive peristalsis. The conspicuity of extravasated CEB is also dependent on the extent of enhancement of the mucosa on which it falls. To determine if CT can play a role as a noninvasive accurate approach in the identification of active lower GI tract bleeding, such problems must be addressed.
The purpose of our study was to evaluate the feasibility of helical CT as an imaging modality for depicting active colonic hemorrhage in a swine model.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODS RESULTS DISCUSSIONAPPENDIX REFERENCES |
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The CEB was composed of approximately 100 mL of blood that was removed from each swine during the examination and anticoagulated with ethylenediaminetetraacetic acid. After the scanner was calibrated with a water phantom, 10 mL of blood was adjusted to a fixed conservative attenuation level of approximately 140 or 180 HU by adding contrast material (Ioxilan; Cook) with a concentration of 350 mg of iodine per milliliter.
Each swine was then placed in a supine position and put into a helical CT scanner (HiSpeed Advantage; GE Medical Systems, Milwaukee, Wis). The syringe containing CEB was loaded into a calibrated syringe pump (Lomir Biomedical, Quebec, Canada) that had digitally selectable infusion rates. This syringe was then connected to a microcatheter (Tracker-18; Boston Scientific), which was then introduced into the guiding cannula through a Tuohy-Borst adapter (Guidant, Temecula, Calif) with its tip placed 1 mm beyond the tip of the guiding catheter. Prior to this, the microcatheter had its radiopaque tip removed. A second syringe containing unopacified anticoagulated blood was placed into a second identical syringe pump and connected to the side arm of the adapter. The guiding cannula was then filled or "primed" with unopacified blood, its volume having been calculated previously. Both pumps were set to the same infusion rates. Figure 1 is a simplified schematic of the general configuration of the catheters and pumps.
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In two examinations, after reliable depiction of intraluminal CEB extravasated at a rate of 0.5 mL/min onto mucosa containing unopacified blood, the microcatheter-guiding system was transferred to a more distal location in the descending colon. To stimulate colonic peristalsis, a solution of 10 mg of bisacodyl (Fleet, Lynchburg, Va) in 30 mL of suspension was injected into the short rectal catheter (Fig 1). Ten milliliters of unopacified blood was again predeposited at the extravasation site via the guiding cannula, followed by a repeat examination that used similar parameters to see what effect, if any, hyperperistalsis would have on the CEB dilutional process. Overall, a total of 16 examinations were performed in 14 swine with CEB set at either 140 (n = 8) or 180 HU (n = 8). Of the 16 examinations, nine were performed with CEB extravasated onto a solid surface (defined as naked mucosa or fecal debris) and seven were performed with CEB extravasated onto a liquid surface (defined as mucosa with a 10-mL pool of previously extravasated unopacified blood).
CT Examination
CT examination of the simulated bleeding site was performed as follows: An initial CT scout image of the abdomen was obtained, and the affixed radiopaque bands helped to identify the location of the otherwise radiolucent catheter. Sequential helical images that were 3 mm thick were then obtained by using 120 kVp, 180 mA, and a pitch of 1.5. Imaging was performed over a 5-cm length in the z axis centered at the tip of the microcatheter. CT scanning was initiated 5 seconds after the completion of 30 seconds of extravasation of CEB. The imaging sequence was completed in 15 seconds and was then immediately repeated five more times. Overall, six imaging passes were completed through the targeted volume over an elapsed time of 95 seconds after the end of the extravasation of CEB and during active extravasation of unopacified blood. A single delayed scan centered at the guiding cannula tip was obtained at 220 seconds. This overall imaging protocol allowed us to determine if the extravasated CEB could be imaged and, if so, its dilution over time. This protocol would obviously not be used in a clinical setting, but it allowed experimental data of the dilution process of extravasated CEB to be used later for our mathematical modeling.
Mathematical Modeling
Our initial goal was to obtain parameters to mathematically model the dilution of extravasated CEB onto colonic mucosa. As this was a feasibility study, our desire was to maximize the chance of obtaining useful dilution data. Thus, the examinations were performed with ideal conditions, including intravenous administration of 1 mg of glucagon (Bedford Laboratories, Bedford, Ohio) 10 minutes prior to examining each swine to minimize peristalsis-related dilution and to perform an examination during suspended respiration.
A mathematic model of active colonic bleeding was developed by using the experimentally derived dilution data to allow simulation of multiple clinical scenarios without performing an extensive number of examinations. The model had three components and was based on a mass and volume balance of contrast material (iodine) and consisted of (a) a bleeding source (inflow), (b) a dependent pool of extravasated unopacified blood that already existed on the colonic mucosa at the bleeding site and had some initial volume (Vinit), and (c) an outflow from the bleeding source that was caused by peristalsis and egress of blood onto the adjacent bowel. If intravenous contrast material is administered, there is an inflow concentration of iodinated contrast material, defined as ci(t), that is assumed to extravasate from the arteriole at a constant bleeding rate into the pool. Mixing of the inflow into the pool is assumed to be uniform and instantaneous and yields a pool concentration of iodinated contrast material, defined as c(t). The pool loses volume at a rate defined as dvo(t)/dt. The concentration of the outflow is the same as the concentration within the pool. In the Appendix, the mass balance (Eq [A1]) and the volume balance (Eq [A2]) of this model are given, and from these, the general differential equation (Eq [A4]) is derived, which governs the dilutional process of extravasated CEB.
The detectability of extravasated CEB is dependent on its conspicuity relative to adjacent contrast material–enhanced colonic mucosa. To build this into our mathematic model required consideration of the dilution of CEB as a function of time, which is simply a time-attenuation curve (TAC) of the CEB, compared with the TAC of the colonic wall. Because porcine colonic mucosa was found to be less than 1 mm thick, an accurate TAC could not be generated; therefore, a TAC for colonic mucosa was generated from human data obtained from five healthy patients who were being considered as renal donors. Institutional Review Board approval and informed consent were not required, and after an initial unenhanced CT examination of the abdomen and pelvis (5-mm section thickness, pitch of 2, 140 kVp, 300 mA), patients underwent dual-phase helical CT while receiving approximately 2 mL/kg body weight of contrast material (Ioversol 350; Mallinckrodt, St Louis, Mo) delivered at a rate of 3.5 mL/sec via an antecubital vein. No patient received a dose of less than 100 mL or more than 150 mL. Oral administration of contrast material consisted of water only. While the patient performed a breath hold, 2.5-mm-thick images (140 kVp, 300 mA) were acquired from the celiac axis through the kidneys after a 30-second delay, followed by acquisition of 5-mm-thick images (140 kVp, 340 mA) of the abdomen and pelvis starting 70 seconds after the injection of contrast material. Finally, at a single transverse level of the abdomen that depicted the descending colon in a vertical orientation (chosen on the basis of a review of earlier images), a single 5-mm-thick image was obtained at 120 seconds. Measurements of the proximal descending colon were obtained from each image for each patient by using a crosshair, which measures individual pixel attenuation in Hounsfield units. All measurements were performed by a single individual (R.G.S.). The crosshair was centered within the colonic lumen and sequentially moved across the bowel wall to the surrounding pericolic fat. The maximum pixel attenuation achieved (assumed to be enhancing colonic mucosa) was noted. This procedure was performed three times for each image, and the average maximum pixel attenuation was recorded. This attenuation value was then compared with the time of image acquisition to yield a colonic TAC for each patient. TACs were then combined to yield a single TAC to be used for our model.
Equation (A4) represents the dilution process of extravasated CEB but assumes that CEB has a constant level of enhancement. In reality, CEB has a variable level of enhancement over time that, because our model assumes the bleeding source to be a colonic arteriole, mimics aortic enhancement. Aortic enhancement is assumed to follow Equation (A7), which is a gamma-variate function and has been shown to reasonably approximate an in vivo arterial TAC (4); hence, the same group of patients mentioned previously underwent acquisition of aortic enhancement over 13 time points. By using individual images, a single region of interest of at least 25 mm2 for each time point was acquired for each patient, and individual aortic TACs were generated. The individual aortic TACs were combined by averaging attenuation values at each time point to yield a single aortic TAC that was then fitted to Equation (A7) to yield 
and ß.
Combining Equations (A4) and (A7) yields Equation (A9), which represents the final equation governing the modeling of active colonic arterial bleeding. A value of Vinit of Equation (A9) can be determined from the seven sets of images from each swine examination, which are seven samples of c(t) of Equation (A8b) and represent our CEB dilution process.
Data Analysis
For each successful swine examination in which extravasated CEB was depicted, images were evaluated at a workstation with software (Advantage, Version 2.0.18; GE Medical Systems). In each experiment, a region of interest of at least 15 mm2 was applied (W.G.K.) to the visible extravasated CEB three times, and the mean attenuation and associated time were documented. A region of interest of the preextravasation background site was also obtained, and a final CEB dilution curve or, more simply, a CEB TAC was generated. By using a constrained, nonlinear least-squares algorithm (5), Equation (A8b) was optimally fit to each TAC. Curve fitting was performed with software (Matlab version 5.2, Optimization Toolbox; Mathworks, Natick, Mass) that employs a parameter optimization program. All fitting was performed for attenuation data that directly translated to iodine concentration data (6). The model parameters derived from the fitting were defined as c(30), the iodine concentration at the extravasation site at 30 seconds, and Vinit, the effective volume of the pool of initial unopacified blood that is required to solve Equation (A9).
The initial rise of human aortic TAC was optimally fit to the gamma-variate function (Eq [A7]) by using the Levenberg-Marquardt algorithm (7,8). In doing so, the parameters and ß were determined. Equation (A7) also contains a scaling factor (L), which is a constant that can be varied and directly relates to peak aortic enhancement, as per the work of Burbank et al (9,10). Of note, the tail of the aortic TAC was not considered, because the gamma-variate does not adequately model the tail of aortic enhancement data because of neglecting recirculation effects, as per the work of Thompson et al (4).
Simulation of Detection of Bleeding
Equation (A9) gives the modeled in vivo concentration of iodine (or, equivalently, the enhancement in Houndsfield units) of the extravasated CEB as a function of time. Graphic presentation of Equation (A9) is simply the TAC for our modeled extravasted CEB. Point-by-point subtraction of the bowel wall TAC from the CEB TAC yields the conspicuity curve of the extravasated CEB as a function of time (ie, conspicuity[t] = c[t] - bowel wall enhancement[t]). The conspicuity curve must rise above a certain threshold before the extravasated CEB can be detected; however, conspicuity, as described here, assumes optimal CT imaging of the extravasated CEB (ie, the extravasated CEB is centered within a reconstructed plane). In practice, this is not necessarily true. The spatial resolution along the z axis is less than the in-plane spatial resolution with the current generation of helical CT scanners; hence, a worst-case scenario occurs if our bleeding focus is located exactly halfway between reconstructed planes (9). In this circumstance, the attenuation and conspicuity of a small volume of the extravasated CEB on enhancing mucosa are effectively lowered.
This partial volume problem has been addressed in the work of Kalender et al (11,12), who showed that there was a loss of attenuation of an imaged sphere with variable diameter, the loss being maximum when the sphere was located exactly halfway between reconstructed planes. Attenuation loss, as shown by these same authors, depends on scanner pitch and reconstruction interval. We believed it was necessary to apply this concept to our study; therefore, we assumed our CEB extravasated in the form of a sphere (with volume = k · t = [
/6] · D3) where k is the bleeding rate in milliliters per minute, t is the time referenced to the initial appearance of extravasated CEB, and D is the sphere diameter. The work of Kalender et al (11,12) shows that the attenuation of extravasted CEB onto colonic mucosa (c[t]) should be multiplied by a contrast reduction factor that is less than or equal to one. Of note is that the contrast reduction factor is dependent on time (t) in addition to being dependent on pitch (p) and reconstruction interval (r). More realistically, therefore, the conspicuity of our extravasated CEB is represented by the following equation, which will be used in our final simulations: Conspicuity(t) = contrast reduction factor(t,p,r) · c(t) - bowel wall enhancement.
With knowledge of and ß, Equation (A9) can be solved with numerical integration to yield c(t) once a bleeding rate k, values for Vinit and L, and, thus, peak aortic enhancement are chosen. For simplicity, collimation and image reconstruction interval were held constant at 5 and 3 mm, respectively, while pitch was varied between 1.5 and 2.0 by adjusting the contrast reduction factor. Because Vinit represents the effective local liquid volume into which extravasated CEB is mixed, it is directly proportional to the rate of buildup and clearance of extravasated CEB. Since extravasation in the clinical setting is most likely to occur onto mucosa that is free of debris (due to hyperperistalsis from active bleeding) but contains preexisting unopacified blood, and because we wished to obtain the most conservative estimate of the rate of bleeding detectable with helical CT, the largest Vinit experimentally obtained for a liquid surface (1.1687 mL) was used in all simulations. Hence, for a chosen set of input variables (pitch, bleeding rate [k], and peak aortic enhancement), c(t) was solved for and a conspicuity curve was generated.
On the basis of work by Seeram (13), a minimum conservative conspicuity threshold of 20 HU was used. This threshold was applied to each conspicuity curve that was generated to allow us to determine if the resultant extravasated CEB was visible and, if so, the window of time that visibility was present.
Statistical Analysis
To validate our mathematic model and all the assumptions made in generating Equation (A8b), the modeled CEB dilution process must correlate with the experimental dilution process for each experiment. To assess this, once the parameters c(30) and Vinit were determined for each experiment, the Matlab software automatically used these parameters, created a modeled CEB TAC, and statistically evaluated its fit to the experimental data. Maximum regression values (R2), which represent the sum of the correlation between the experimental and modeled values of c(t), were generated for each animal experiment, with a maximum value of 1.0 indicating a perfect fit.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODS RESULTS DISCUSSIONAPPENDIX REFERENCES |
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and ß. Note how the tail of the gamma-variate causes underestimation of aortic enhancement because of failure to consider recirculation of contrast material. The parameters and ß relate the extent of aortic enhancement to the enhancement of the extravasted CEB in our model. The human colonic wall attenuation data are also plotted in Figure 4. The mean attenuation of the colonic wall was 26.2 HU. It appears that once colonic wall enhancement is achieved, it persists without substantial change over time.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODS RESULTS DISCUSSIONAPPENDIX REFERENCES |
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The results of our study also indicate that the sensitivity of helical CT in depicting active lower GI tract bleeding may exceed the lower limit of 0.5 mL/min cited for mesenteric angiography (2), even under worst-case conditions. Additionally, the reported sensitivity of a 99mTc red blood cell examination in depicting active bleeding ranges from 0.04 to 0.2 mL/min, depending on the duration of patient imaging (15). The ability of helical CT to depict active colonic hemorrhage may, hence, approach that of 99mTc red blood cell scanning while potentially allowing better localization of the bleeding site.
Our estimates of the detectable rates of active colonic arterial bleeding with CT have been based on application of worst-case scenarios. If, for example, we relaxed our conspicuity threshold from 20 to 15 HU and all else remained constant, the detectable bleeding rates in our simulations would theoretically improve by 30%. If the images are reconstructed every 1 mm instead of every 3 mm and all else remains constant, the sensitivities would improve by 100%. For example, at 100 HU of aortic enhancement, pitch of 2.0, collimation of 5 mm, image reconstruction interval of 1 mm, and conspicuity threshold of 20 HU, the minimum detectable rate of extravasation potentially decreases from 0.4 to 0.2 mL/min. These sensitivities are certainly competitive with those of 99mTc red blood cell examinations and indicate that clinical application of helical CT for depicting active colonic bleeding should be pursued.
The overall excellent fit between the experimentally derived CEB dilution curves and the mathematically derived curves for both solid and liquid extravasation surfaces attests to the accuracy of the assumptions made in creating our mathematic model. This excellent fit also helps validate the conclusion resulting from the application of our model, that helical CT can be sensitive in depicting low rates of active colonic bleeding. Also, the mathematic model and computer simulation of the bleeding and detection process allowed efficient and economic extension of the experimental data to a wide variety of conditions. For example, independently varying the pitch, peak aortic enhancement, and rate of extravasation were all carried out quickly. In addition, the coaxial catheter system used to simulate bleeding did not perform at rates of extravasation below 0.3 mL/min because of surface tension effects. Our validated mathematic model, however, allowed us to study bleeding rates below 0.3 mL/min.
Theoretical Limitations
Multiple potential limitations to our study exist. First, the dilutional process resulting from extravasation of CEB onto swine colon was assumed to be similar to that of humans (ie, the worst-case Vinit derived from our swine examinations was combined with human aortic and colonic wall enhancement data in our computer-based simulations). We believe, however, that the underlying physical process of dilution of extravasated CEB—that is, the extravasation into solid material or a pool of previously existing unopacified blood followed by continued extravasation of unopacified blood—should logically be similar. Additionally, Stevens et al (16) concluded that the colon of swine is structurally more similar to the colon of humans than the colon of other mammals; therefore, the swine model was chosen because it was most optimal. We also believe that the dilution process of extravasated CEB would be similar whether resulting from our microcatheter system or from a true mucosal injury. For these reasons, we believe our results are clinically relevant.
Another possible shortcoming of our study was the modeling of the human abdominal aortic TAC with the gamma-variate function, which caused underestimation of the tail of the TAC because it does not take into account recirculation of contrast material. The literature shows, however, that use of the gamma-variate for all but the tail of the aortic TAC appears to be reasonable (4). Also, in clinical practice, recirculation of contrast material would maintain some level of enhancement of extravasated blood for a longer period of time than our model allowed. Thus, by using the gamma-variate function, the enhancement of CEB actually declined at a faster rate and was followed sooner by unopacified blood, which led to an even more conservative estimate of helical CT for the depiction of active colonic bleeding. Other methods of modeling the aortic TAC exist (6,17), but the gamma-variate function is well established and has been shown to correspond well to empirically derived curves of blood flow (18).
We also wish to point out that the gamma-variate function was fitted to the aortic TAC derived from healthy potential renal donors who received contrast material at a rate of 3.5 mL/sec via an antecubital vein. The work of Burbank et al (9,10) shows that the width of the gamma-variate depends on the central blood volume and the cardiac output. We acknowledge that the experimental and gamma-variate–derived aortic TACs will vary depending on contrast material injection rate, patient size, and cardiac status, but we believe the magnitude of the potentially detectable colonic bleeding rates identified in our work is accurate.
Another potential shortcoming lies in our attempts to estimate contrast enhancement of the colonic wall, or, actually, colonic mucosa. For the sake of thoroughness, we believed it was necessary to consider the actual conspicuity of extravasated CEB onto enhancing colonic mucosa to simulate a true clinical situation. We know of no study that assessed colonic wall enhancement directly, and we admit our method may not be optimal. The thickness of the colon wall does not lend itself to accurate placement of a sizable region of interest. Performing pixel-by-pixel analysis of the wall and using maximum pixel attenuation at a given time gave us the maximum possible colonic wall TAC and, thus, the worst-case scenario for the conspicuity of our extravasated CEB.
Finally, for the sake of simplicity, the simulations assumed that the extravasated CEB formed a spherical collection. Of course, no extravasated CEB actually assumes a spherical shape. This assumption can be considered another worst-case scenario, however, because the surface area of any given volume is minimized when the volume is spherical and, therefore, is least visible on two-dimensional transverse images. In addition, the location of the extravasated CEB was assumed to be in the worst location in our simulation program, that is, located halfway between reconstructed planes.
We wish to point out that the TAC of the enhanced blood entering the bleeding colonic arteriole was assumed to mimic the abdominal aortic TAC. This assumption is supported by examinations performed in the pulmonary arterial bed of dogs that showed dispersion of contrast material occurred only within the capillary bed and not within the conducting arteries (19). Also intuitively, there is no reason to suspect that the iodine concentration within blood should change during transport from the abdominal aorta to the mesenteric vessels.
Clinical Limitations
Clinical limitations of a CT examination for bleeding can exist. As with other imaging examinations for GI tract bleeding, a false-negative result may occur because of the intermittent nature of lower GI tract bleeding, as demonstrated by Sos et al (20). Also, a potentially inherent problem with a CT examination for bleeding may lie in the clinical difficulty in discerning between active colonic and small-bowel bleeding. We believe that CT may not be efficacious in the setting of small-bowel hemorrhage. Active extravasation may be difficult to identify in a collapsed small bowel, which can also show bowel wall enhancement up to 60 HU (21). Thus, we surmise that a CT examination with negative results for bleeding may not have the diagnostic power of either angiography or 99mTc red blood cell scanning, either of which should be considered first if small bowel bleeding is suspected.
Practical Considerations for Performing a CT Examination for Bleeding
Our findings suggest several practicalities that should be considered when performing a CT examination for bleeding. We believe that no oral contrast material should be given. We also believe that the sensitivity of the examination may be improved with colonic insufflation. Glucagon may also help minimize peristalsis during the examination. We observed this in our animal examinations, even in the two instances in which bisacodyl was administered in an effort to exacerbate peristalsis. An unenhanced examination of the abdomen should be performed first, followed by bolus timing of the contrast material through the superior mesenteric artery to tailor the scanning delay to each patient. From our experience, we conclude that adding 20 seconds to the time of peak enhancement of the superior mesenteric artery after a test bolus should allow sufficient extravasation for detectability when bleeding is occurring at a rate of 0.4 mL/min or higher. Obviously, this is a general recommendation and will depend on the speed of imaging (single– vs multi–detector array CT). Side-by-side comparison of unenhanced and contrast-enhanced images should then be performed. Reexamination during the same sitting should also be contemplated if the initial scan is negative for colonic hemorrhage.
Practical applications: By using a combination of experimental examinations and mathematic modeling, we have shown that helical CT has the potential to depict active colonic arterial bleeding at a rate below 0.5 mL/min. The theoretical logistical problems such as image timing and conspicuity of a small volume of extravasated contrast material do not appear to be major limitations according to our results, which makes helical CT a potentially viable and noninvasive modality for the assessment of active colonic hemorrhage in a selected patient population. Additional advantages of CT may include localization of the bleeding site and demonstration of intraabdominal abnormalities that may be the cause of bleeding. It is our hope that with additional studies, an examination with CT for GI tract bleeding can also be shown to be as specific as an examination with 99mTc red blood cell scanning in excluding active bleeding.
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APPENDIX |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODS RESULTS DISCUSSIONAPPENDIX REFERENCES |
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Assume that dvo/dt and dvi/dt (the bleeding rate) are constant. Also, make the following substitutions: m = cv, mi = civi, and mo = covo, where c is the iodine concentration of the pool as a function of time, co is the iodine concentration of the outflow as a function of time, and ci is the iodine concentration of the extravasating blood as a function of time.
Assume also that co is equal to c. Manipulation of Equations (A1) and (A2) with these substitutions yields
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Because the bleeding rate is assumed to be constant, the following substitution is made:
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In addition, from Equation (A2), it follows that
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Making these substitutions to Equation (A3) yields, after manipulation,
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Equation (A4) is the general differential equation that governs the dilution process. This equation is known as a linear first-order equation, which is solved by using the integrating factor
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In the simulated bleeding as done in the examinations, a contrast material–blood admixture is extravasated for 30 seconds, followed by extravasation of unopacified blood thereafter. Therefore, ci(t) assumes the following form:
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t 30 seconds and
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In vivo, ci(t) is assumed to conform to the form of a gamma-variate function:
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0, L is a constant scaling factor having units of concentration, and and ß are arbitrary real, positive parameters of the gamma-variate. is dimensionless, and ß has units of time.
For the simulated bleeding, substituting Equation (A6) into Equation (A4) yields the following piecewise continuous, closed-form solution:
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t 30 seconds, and
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Equation (A8b) indicates that the concentration of extravasated iodine within the pool undergoes hyperbolic, not exponential, dilution.
For the in vivo setting, substituting Equation (A7) into Equation (A4) and reducing gives
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Equation (A9) has no explicit solution for c(t); therefore, it is numerically integrated to determine c(t).
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FOOTNOTES |
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Author contributions: Guarantors of integrity of entire study, R.G.S., W.G.K.; study concepts, W.G.K.; study design, R.G.S., W.G.K.; literature research, R.G.S., W.G.K.; clinical studies, R.G.S.; experimental studies, R.G.S., W.G.K.; data acquisition and analysis/interpretation, R.G.S., W.G.K.; statistical analysis, W.G.K.; manuscript preparation, definition of intellectual content, editing, revision/review, and final version approval, R.G.S., W.G.K.
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REFERENCES |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODS RESULTS DISCUSSIONAPPENDIX REFERENCES |
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R. M. Summers Science to Practice: Detection of Active Colonic Hemorrhage with Use of Helical CT: Findings in a Swine Model Radiology, September 1, 2003; 228(3): 599 - 600. [Full Text] [PDF]
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) time-attenuation (dilution) data of extravasated CEB onto a liquid surface in swine colon. An R2 value of 0.9134 indicates an excellent fit of the modeled curve to the experimental curve.
